The doohickey keeps tension on the engine balancer chain. The "adjuster bolt" is under that rubber plug by the shift lever.
I've noticed the Owner's Manual calls for adjustment of the balancer chain every 7,500 miles but doesn't tell you how to do it. I personally adjust mine at every oil change as I feel the 7,500-mile interval is way too long.
In a nutshell, you slightly loosen the bolt under that rubber plug. That "unclamps" the balancer lever, allowing the spring to pull the lever to tension the chain, then you snug the bolt back down to hold everything in place until the next adjustment.
That's how it should work in theory, but a lot of people who have upgraded their doohickey have found that the factory coil spring quickly runs out of action so when you loosen the bolt, there's not enough strength left in the spring to actually move the lever to increase tension on the chain. That's why a lot of people "do their Doo" and switch to an aftermarket setup to ensure the adjustment procedure actually results in something being adjusted.
I chose the torsion spring option as it should theoretically never run out of tension to adjust that lever.
Since you can't see any of this happening inside the engine, you can never be sure your adjustment is actually doing anything. With a known, reliable spring attached to the lever, chances are everything's doing what it's supposed to in there.
When I do mine, I lean it to the right and whack the case with a rubber/plastic mallet to make sure everything jiggles around and does what it's supposed to. Does it work? I don't know, but it makes me feel better.
pdwestman advocates setting the engine to TDC before performing this procedure. He knows a lot more about motorcycles than I do and it makes sense to me so I'm going to start doing the TDC-indexing thing prior to performing the adjustment procedure since it's easy to do.
I would recommend picking up a dedicated maintenance manual like a Clymer or Kawasaki Service Manual. It's important to not loosen that adjustment bolt too much and also not to overtorque it when you tighten it back down.
Kind of a layman's description of the whole deal, but maybe this will give you an overview of what it's all about.